At a sports festival half the number of people that chose basketball, chose football. The number of students who chose basketball was a quarter the number of students who chose baseball. There were 84 more students who chose baseball than soccer. How many chose basketball?
Let's break down the information given step-by-step:
1. Let's assume the number of students who chose basketball is "x".
2. The number of students who chose football is half the number of people who chose basketball, so it is (1/2)x.
3. The number of students who chose baseball is four times the number of students who chose basketball, so it is 4x.
4. The number of students who chose soccer is 84 less than the number of students who chose baseball, so it is 4x - 84.
Now, let's set up an equation to solve for "x":
x + (1/2)x + 4x + 84 = total number of students
Combining like terms:
6.5x + 84 = total number of students
To find x, we need to know the total number of students, which is not specified in the given information.
To find out how many students chose basketball, let's break down the information provided step by step:
1. Let's assume the number of students who chose basketball is "B."
2. According to the given information, half the number of people that chose basketball also chose football. Therefore, the number of students who chose football is "B/2."
3. The number of students who chose basketball is a quarter of those who chose baseball. So, the number of students who chose baseball is "4B."
4. It is also mentioned that there were 84 more students who chose baseball than soccer. Hence, the number of students who chose baseball is "84 + S," where "S" represents the number of students who chose soccer.
Now, let's form an equation to solve for the number of students who chose basketball:
B/2 = 4B - (84 + S)
Simplifying the equation, we get:
B/2 = 4B - 84 - S
Multiplying both sides by 2 to eliminate the fraction:
B = 8B - 168 - 2S
Rearranging the equation:
7B = 168 + 2S
From this equation, we can see that "B" depends on "S." Therefore, we need additional information to determine the exact number of students who chose basketball.